MATHEMATICS · Multi-part · AP · Calculus AB · Applications of Integration · Applications of Integration
Problem
Consider the region enclosed by the parabola y=x2, the horizontal line y=4, and the vertical lines x=−1 and x=1.
(i) Draw a rough sketch of the region and clearly mark all the intersection points of the bounding curves and lines.
(ii) Justify, with reasons, whether integrating with respect to x or with respect to y is more convenient for computing the area, and state which portions (if any) must be treated separately.
(iii) Write the complete definite integral (or sum of integrals) required to obtain the area of the region. Do not evaluate the integral(s).